Environmentally Liable Multi-Objective Multi Time Span Fuzzy Fractional Capacitated Transportation Problem in the Two Echelon Supply Chain with Heterogeneous Items and Mixed Constraints

Abstract

In today’s world supply chain is an integral part of business. This paper proposed a model of environmentally liable multi-objective multi time span fuzzy fractional capacitated transportation problem (ELMOMTHIFFCTP) in the two echelon supply chain with heterogeneous items and mixed constraints. In this model, few objectives are considered as a linear function and few are fractional functions. Especially the objective function related to emission cost is considered as linear fractional objective function. The damage cost, labor cost, packing cost and quality cost are considered as triangular intuitionistic fuzzy numbers. This paper focuses on minimization of damage cost, labor cost, quality cost, packing cost and the ratio related to transportation cost , inventory carrying cost and emission cost of the entire supply chain. An industrial case demonstrates the feasibility of applying the proposed model to real world problem in a two – echelon supply chain under uncertain environment also determine an optimal inventory level for the warehouse and distribution centers using fuzzy programming approach through LINGO software.